It was the second major victory of the 39-year-old American's career, following his U.S. Masters triumph in 2007, but he was keen to put his achievements in perspective.
"This isn't going to define me or my career, at least I hope it doesn't," the down to earth Johnson told reporters at St Andrews. "It's not my legacy.
"Granted, as a professional athlete and as a golfer I'm going to relish this, I'm going to savour this. I'm humbled by this but my legacy should be my kids, my family, that kind of thing.
"I realise it's just a game. I'm just a guy from Iowa that has been blessed with a talent and this game provides great opportunity," added Johnson.
"If you look at it that way it kind of takes the pressure off. I don't want to make it any bigger than what it should be."
Johnson spared a thought for fellow countryman Jordan Spieth, 21, who was one of the first to congratulate him despite feeling disappointment at failing to add the British Open to his wins this year at the U.S. Masters and U.S. Open.
"He is a really good friend of mine," said Johnson. "Granted, he's 18 years younger than me, which is perspective.
"I can't describe the magnitude of what he was going through because I've never been in that position. We haven't really seen that with the exception of Tiger (Woods).
"Jordan could be sitting here now...to have a champion like him take the time to give me best wishes...speaks volumes. He's a phenomenal talent and I'm telling you right now...he's a better person than he is a golfer."
Johnson also took time out to praise world number one Rory McIlroy who was sidelined for the British Open after injuring ankle ligaments playing soccer with his friends.
"There's not a person that anybody would rather have here than Rory," the American said. "He's certainly taken the game to newer heights as of late.
"It's really unfortunate. We all want him back and back healthy more than anything."
(Editing by Justin Palmer)
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